If pathogen species, strains or clones do not interact, intuition suggests the proportion of co-infected hosts should be the product of the individual prevalences. Independence consequently underpins the wide range of methods for detecting pathogen interactions from cross-sectional survey data. Surprisingly, however, the results of the very simplest of epidemiological models challenge the underlying assumption of statistical independence. Even if pathogens do not interact, death and/or clearance of co-infected hosts causes net prevalences of individual pathogens to decrease simultaneously. The induced positive correlation between prevalences means the proportion of co-infected hosts is expected to be higher than multiplication would suggest. By modeling the dynamics of multiple non-interacting pathogens, we develop a pair of novel tests of interaction that properly account for this hitherto overlooked coupling. Which test is appropriate for any application depends on the form of the available data, as well as the extent to which the co-infecting pathogens are epidemiologically similar. Our tests allow us to reinterpret data from a number of previous studies, including pathogens of plants and animals, as well as papillomavirus and malaria in humans. We find certain reports of interactions have been overstated, and in some cases are not supported by the available data. Our work demonstrates how methods to identify interactions between pathogens can be updated to account for epidemiological dynamics.